Biosensor with integrated antenna and measurement method for biosensing applications

ABSTRACT

The present invention relates to a biosensor (1) which enables the concentration of a desired molecule inside a liquid in the medium, and essentially comprises at least one metallic plate (2) which functions as a ground plate, and which is preferably manufactured from aluminum, at least one dielectric substrate (3) which is located on top of the metallic plate (2), at least one split-ring resonator (4) which is realized on top of the dielectric substrate (3), and which is coated with a dielectric layer, at least two symmetrical antennas (5) which are realized on the same plane with the split-ring resonator (4) on the substrate (3), at least two ports (6) where a network analyzer is connected with the antennas (5) via SMA (SubMiniature Version A) connectors.

CROSS REFERENCE

This application is the continuation application of U.S. patentapplication Ser. No. 15/511,647, filed on Mar. 16, 2017, which isnational phase of International Application No. PCT/TR2015/050101, filedon Sep. 14, 2015, which is based upon and claims priority to TurkishPatent Application No. 2014/11254, filed on Sep. 24, 2014, the entirecontents of which are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to a sensor (BioSRR) operating inmicrowave frequencies. More specifically, a split-ring resonator withintegrated antennas is disclosed. The said sensor can be used in fieldof detecting biomolecules.

BACKGROUND

Split-ring resonators (SRR) have been widely used for applications inelectromagnetic spectrum spanning from microwave to photonicfrequencies. SRR structure defines a basic inductance-capacitance (LC)resonator electrically. The resonant frequency of the resonator isdetermined with the geometry of the structure. The structures whosedimensions are measured by millimeter and centimeters are generally usedfor applications in microwave frequency. Structures in micrometer-scaleare used for terahertz frequencies, while smaller structures innanometer-scale work in infrared and the visible light spectrum. WhenSRR structures are excited appropriately, the magnetic permeabilitybecomes negative within the vicinity of the resonant frequency of thestructure. This property is used for developing extraordinary propertiessuch as negative index of refraction.

Unlike other passive resonator tanks, SRR structures can exhibit sharpresonant behavior with quality factor 1000 and above in microwavefrequencies. Thus, the changes in resonant frequency of SRR structurescan be used as a very effective sensing mechanism. The strain sensorsworking on this basis have been demonstrated in the literature. Thechanges in SRR geometry due to strain change the resonant frequency ofthe structure, and this change is measured. Further, the resonantfrequency is sensitive to change in dielectric constant of the medium inwhich the structure is present. This property has also been used formicrofluidic applications. The geometry of the structure does not changein these applications, however the changes in dielectric properties ofthe medium in which it is present result in changes in the effectivecapacitance of the SRR structure, therefore the resonant frequency ofthe structure shifts. Biosensors using this mechanism have also beendeveloped. Biomolecules binding on the surface of SRR structures altersthe dielectric constant of the structures. SRR structures used withmicrostrip lines have been demonstrated for applications of hormone andantigen detection. Similar structures have been used for measuringbiotin-streptavidin interaction and DNA hybridization.

External antennas are used for electrical excitation of SRR structuresin the state of the art. The alignment of these antennas imposes animportant limitation to realize portable sensors. In addition, largeexternal antennas are not suitable for integration with electronicchips.

The transmission (s21) characteristic (s21 spectrum) of SRR structuresdemonstrated in the current technique exhibits a sharp dip at resonance.The shift of this dip frequency can be measured with measurementequipment such as vector network analyzers. However, it is notadvantageous to use the sensors exhibiting this electrical property aspart of oscillators by integrating with electronic circuits.

Korean Patent Document No. KR20140079094 (A), an application known inthe state of the art, discloses a resonator, the electrical parametersof which change under interaction with biomolecules and wherein the saidchange is measured with a measurement method used with the resonator.The measurement method, which requires direct electrical connection tothe resonator structure is different from the inventive system. In theinventive biosensor, direct electrical connection to the resonatorstructure is not required; this structure is excited withelectromagnetic waves. The antennas integrated to the resonator forexcitation can be used with different measurement methods.

European Patent Document No. EP1912062 (A1), an application known in thestate of the art, discloses a structure the electrical capacitance valueof which can change. The said structure is comprised of electrodesdefined on a dielectric substrate. The electrodes are coated withbiomolecules, and the electrical capacitance of the structure changesdue to interaction between biomolecules. The change in capacitance isdetected using an electronic circuit which is used together with theelectrodes. The said disclosed structures are different from theinventive biosensor in terms of both function and structure. Contrary toEP1911206 (A1) disclosing a capacitor, the inventive system suggests anew resonator structure. With the inventive BioSRR method, disclosed isa new resonator operating in microwave band, the surface of which can becoated with biomolecules, integrated with an antenna is disclosed. Thesaid resonator is excited by means of the integrated antennas, and theresonance frequency shifts can be measured.

In the article published as “Displacement Sensor Based on Diamond-ShapedTapered Split Ring Resonator”, IEEE SENSORS JOURNAL, VOL. 13, NO. 4,APRIL 2013, known in the state of the art, a sensor structure has beendeveloped for measuring displacement information on the position and thestructure. The structure is defined in a coplanar waveguide for themeasurements. The electrical characteristics of the structure aremeasured by means of the said waveguide. The sensor disclosed in thisarticle is different from the inventive BioSRR in terms of measurementmethod and the structure.

U.S. Pat. No. 7,964,144 (B1), a patent known in the state of the art,discloses a structure comprised of a pair of electrode structure definedon a substrate and AIN base structure defined in the middle of theelectrodes. The electrodes are used to form a horizontal surfaceacoustic wave and to collect the formed wave. The said method is usedfor different applications in the field, and it is different from theresonator defined with the inventive BioSRR.

In the article published as “Compact size highly directive antennasbased on the SRR metamaterial medium”, New Journal of Physics, 7 (2005)223 in the state of the art, split-ring resonator structures defined onFR4 substrate are disclosed. The frequency responses of these structuresare measured by means of external monopole and horn antennas.Furthermore, these structures are placed inside the antennas, anddirected wave propagation is achieved. The application disclosed in thisarticle is completely different from the inventive BioSRR. Furthermore,the method used to excite the resonator structures in BioSRR method isbased on defining the resonator and the antenna on a single substrate inan integrated manner. These antennas and the structure are excited withhybrid Tem mode wave. On the other hand, resonator and antennastructures in the BioSRR method are defined on top of a dielectricsubstrate that is attached to a metal backplate. The presence of thisbackplate results in the transmission (s21) and reflection (s11)characteristics observed in this article.

The structure disclosed in the article published as“Efficient,Metamaterial-Inspired Loop-Monopole Antenna with ShapedRadiation Pattern”, 2012 Loughborough Antennas & Propagation Conferencein the state of the art is a new antenna. The disclosed antenna iselectrically loaded with a split-ring resonator, and improvements intransmission/reflection characteristic of the antenna are achieved. Theapplication fields of the structure disclosed in this article and theinventive BioSRR structure are different from each other. BioSRR methoddoes not suggest a new antenna structure. A pair of monopole patchantennas integrated to the resonator structure is used for measuring theresonator characteristic. Split-ring resonator is used as a sensorstructure in BioSRR. Furthermore, resonator and antenna structures inthe BioSRR method are defined on top of a dielectric substrate that isattached to a metal backplate. The presence of this backplate results inthe transmission (s21) and reflection (s11) characteristics observed inthis article.

In the article published as “Enhanced transmission of electromagneticwaves through split-ring resonator-shaped apertures”, Journal ofNanophotonics 051812-1 Vol. 5, 2011 known in the state of the art,split-ring resonators are integrated to the waveguides, and used toincrease the electromagnetic permeability of the guide. In thisapplication, the electromagnetic wave propagates along with the normalof the resonator structure, so the incidence angle is 90°. The devicedisclosed in this article is completely different from the inventiveBioSRR in terms of application, structure and function. In BioSRRmethod, it is the antenna pair exciting the resonator, not thewaveguide. The electromagnetic wave propagates perpendicular to thenormal of the resonator, so the incidence angle is 0°.

United States Patent Application No. US20110152725A1, an applicationknown in the state of the art, discloses a structure comprised of planarcoil and split-ring resonators suggested for biological applications.These structures are especially used for displacement measurement.External antennas are used for the measurements. The said measurementmethod is different from the method of using an integrated pair ofantennas with the resonator suggested in BioSRR. Furthermore, theresonator and antenna structures in the BioSRR method are defined on topof a dielectric substrate that is attached to a metal backplate. Thepresence of this backplate results in the transmission (s21) andreflection (s11) characteristics observed in this article.

SUMMARY

The objective of the present invention is to provide a biosensor whereinthe antennas are manufactured on the same substrate with the split-ringresonators (SRR), and this structure is integrated with the electronicreadout circuit. The inventive biosensor is excited by electromagneticwaves. The said electromagnetic wave is provided by means of theelectric signal applied on the antennas that is converted intoelectromagnetic waves. The shift in resonant frequency of the resonatorcan be measured using the receiver antenna and the electronic readoutcircuit; therefore, the concentration of the molecules in the medium canbe measured. By means of the wave moving towards the SRR being on thesame axis with the antennas, a more efficient current can be induced inthe SRR.

The biosensor design provides advantage relative to the previousinventions since it allows realizing a split-ring resonator on adielectric substrate together with the integrated antennas.

The frequency of the peak formed in the electromagnetic transmissionresponse (s21) of the biosensor forms the basis of the detectionfunction. This characteristic originates from the connection of theintegrated monopole antennas and the thick metallic layer present underthe dielectric substrate with the split-ring resonator. This propertycan be exploited to realize an oscillator circuit using the resonator.

The aluminum backplate placed under the substrate of the split-ringresonator is a metal plate, and the reflection (s11) and transmission(s21) characteristics can be changed by means of this plate. By thismeans, the electronic oscillator circuits to which the resonators areintegrated can be achieved.

BRIEF DESCRIPTION OF THE DRAWINGS

A biosensor developed to fulfill the objectives of the present inventionis illustrated in the accompanying figures, in which:

FIG. 1 is the perspective view of the inventive biosensor.

FIG. 2a is the schematic view showing the locations of deionized waterdroplets in volume of 16 μL on the metallic plate in one embodiment ofthe invention.

FIG. 2b is the measured reflection (s11) characteristic.

FIG. 2c is the measured transmission (s21) characteristic.

FIG. 3a is the experiment schematic showing the functionalization ofbiosensors with biomolecules.

FIG. 3b is the reflection (s11) characteristic measured duringexperiments.

FIG. 3c is the transmission (s21) characteristic measured duringexperiments.

FIG. 4 is a curve showing the observed linear decrease in resonantfrequency relative to heparin molecular concentration increase.

The components shown in the figures are each given reference numbers asfollows:

1. Biosensor

2. Metallic plate

3. Substrate

4. Split-ring resonator

5. Antenna

6. Port

F. FGF-2

H. Heparin

L. Water droplet

P. Parylene

K1. Location-1

K2. Location-2

K3. Location-3

K4. Location-4

N. Nominal

s11. Reflection

s21. Transmission

DETAILED DESCRIPTION

A biosensor (1), which enables the concentration of a desired moleculeinside a liquid in the medium, essentially comprises

-   -   at least one metallic plate (2) which functions as a ground        plate, and which is preferably manufactured from aluminum,    -   at least one dielectric substrate (3) which is located on top of        the metallic plate (2),    -   at least one split-ring resonator (4) which is realized on the        dielectric substrate (3), and which is coated with a dielectric        layer,    -   at least two symmetrical antennas (5) which are realized on the        same plane with the split-ring resonator (4) on top of the        substrate (3),    -   at least two ports (6) where a network analyzer is connected to        the antennas (5) via SMA (SubMiniature Version A) connectors.

The three-dimensional schematic of the inventive biosensor (1) is shownin FIG. 1. The inventive biosensor (1) is comprised of a split-ringresonator (4) formed of split metallic ring realized on top of adielectric substrate (3) and two symmetrical monopole antennas (5). Theconnection with the antennas (5) is achieved through ports (6) via theSMA (SubMiniature Version A) connectors. The dielectric substrate (3) ison a metallic plate (2) functioning as a ground plate and preferablymanufactured from aluminum.

In a preferred embodiment of the invention, biosensor (1) is realized ona FR4 substrate (3) which is commonly used for printed circuit boards.In another embodiment of the invention, the substrate (3) of thebiosensor (1) can also be manufactured on dielectric ceramics such asalumina, and mica. The fabrication of the biosensor (1) is realized withstandard printed circuit board methods. After the definition of metallicstructures on the FR4 substrate (3), there is a thin Parylene (P)material deposition process. Parylene (P) is a biocompatible materialused for anchoring the biomolecules on the biosensor. The depositionprocess is performed at room temperature using chemical vapordeposition, and its geometric definition is performed using lithographyand oxygen plasma etching. The resulting metallic structure behaves as akind of LC resonator, and it can be excited with a magnetic fieldperpendicular to its own plane in a frequency known as magneticresonance (f_(m)). Such excitation induces a current circulating aroundthe ring. In accordance with the equivalent modelling with the lumpedelements, the resonant frequency is given by the following equation:

$\begin{matrix}{{f_{m} = \frac{1}{2\pi\sqrt{C_{eff}L_{eff}}}},{C_{eff} = {C_{g} + C_{s}}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

C_(eff) in this equation gives the efficient capacitance, and L_(eff)gives efficient inductance; and these parameters are determined by thegeometric design. Efficient capacitance is determined by two capacitancevalues which are parallel to each other. The first one of these is gapcapacitance modeled with C_(g), its value is given by the followingequation:

$\begin{matrix}{C_{g} = {{ɛ_{eff}\frac{h\;\omega}{g}} + {ɛ_{eff}\left( {h + g + w} \right)}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

h, w and g in this equation is the thickness and width of the metallicstructure, and the slit gap. Capacitance (C_(s)) is associated with thesurface charges changes with r which is the radius of the ring, and itsvalue is given by the following equation:

$\begin{matrix}{C_{s} = {2ɛ_{eff}\frac{\left( {h + \omega} \right)}{\pi}{\ln\left( \frac{4r}{g} \right)}}} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

As it can be seen from equation 2 and equation 3, effective permittivity(ε_(eff)) of the media surrounding the split-ring resonator (4) ispresent as a multiplier in the surface and gap capacitances. In summary,a change in effective permittivity can shift the resonant frequency.

In order to measure the electromagnetic characteristics of thestructure, a pair of identical monopole antennas (5) is realized in thesample plane with the split-ring resonator (4) symmetrically. Theelectromagnetic wave emitted from the antennas (5) is reflected from thealuminum plate (2) used as a ground plane and transmitted to thesplit-ring resonator (4). The emitted wave interacts with the split-ringresonator (4), and significantly increases the transmission (s21) in thevicinity of fm frequency which the resonant frequency of magneticresonance. The said transmission (s21) characteristic was examinedaccording to relative permittivity change, and the sensor applicationswere considered.

A prototype was manufactured in order to be used in biosensingapplications. The details of the application are as follows:

The scattering circuit parameters of the biosensor (1) were measured bymeans of a vector network analyzer. In this process, both reflection(s11) and transmission (s21) parameters were characterized by using SMAconnectors shown in FIG. 1. Reflection (s11) and transmission (s21)measurements were repeated by placing deionized water droplets (L) todifferent points of split-ring resonator (4) coated with a thin layer ofParylene (P). The volume of each water droplets (L) was measured as 16μL with 2% precision. The location of the points on the split-ringresonator (4) at which the droplets are placed is shown in FIG. 2a .Deionized water droplets (L) increase the gap capacitance or surfacecapacitance according to their location on the split-ring resonator (4).

The reflection (s11) and the transmission (s21) characteristics of thisexperience are given in FIG. 2b . The characteristic measured when thereis no droplet (L) on the biosensor (1) and called as nominal (N) createda resonant frequency with a value of 2.12 GHz. The measured reflection(s11) is high until the resonant frequency due to ground plate, and thereflection decreases sharply at the resonant frequency. The transmission(s21) is low outside of the resonant frequency where it peaks.

The resonant frequency of the metallic ring decreases due to relativepermittivity increases created by the deionized water droplets (L). As acontrol experiment, deionized water droplets (L) were dried andmeasurement was repeated; and it was experimentally seen that theresonant frequency returned to the nominal value (N).

When Location-1 (K1) and Location-2 (K2) given in FIG. 2a are loadedwith deionized water, because they are on the same symmetry axis, thebiosensor (1) shows minimal shift in resonant frequency (1%). Since theLocation-1 (K1) is present on the split ring resonator (4) gap,deionized water dropped on this point both changes the gap and surfacecapacitance. The dominant capacitance of the split-ring resonator (4)mentioned here is the capacitance originated from the surface loads.Larger shifts in the resonance frequency occur when the deionized waterdroplets (L) are placed in Location-3 (K3) and Location-4 (K) points.The change in relative frequency in this case corresponds to 14.5%.Since the biosensor (1) is reciprocal, the same results were obtainedwhen the ports (6) of the network analyzers are interchanged.Furthermore, we should state that the electromagnetic wave emitted fromthe antennas (5) is not planar and the location of the antennas affectsthe resonant characteristic.

Biomolecular measurements were performed in order to demonstrate the useof split-ring resonator (4) based biosensor (1) as biosensorexperimentally. In these measurements, the interaction between the FGF-2(fibroblast growth factor 2, F) and heparin (H) was monitored.Specifically, prepared Murine recombinant FGF-2 (F) and low molecularweight heparin (H) molecules (Enoxaparin, Sanofi, Paris, France) wereused in the experiments. FG-2 (F) is known as a molecule playing animportant role in biological processes such as embryogenesis,angiogenesis and wound healing. Heparin (H) binds the FGF-2 (F)molecules through a specific domain with high affinity.

The experiments started with measuring reflection (s11) and transmission(s21) spectra. The surface of the biosensor (1) coated with parylene (P)was incubated with FGF-2 (F) molecules in a certain concentration (forexample 140 μg/ml). A droplet in volume of 10-μL was placed onLocation-4 (K4) at room temperature and left there for 30 minutes.Therefore, the area subjected to incubation was uniformly coated withFGF-2 (F). In the next step, the surface was dried and heparin (H)droplet in a certain volume and concentration (in volume of 20 μL, andin concentration of 10 μg/ml) was placed. The schematic of theexperiment is shown in FIG. 3a . Then, the surface was dried again andthis time a drop of heparin (H) molecule in volume of 20 μL and inconcentration of 20 μg/ml was placed. This experimental cycle continuedincreasing the heparin (H) concentration. In each step, reflection (s11)and transmission (s21) spectra were measured. The recorded spectra aregiven in FIG. 3b and FIG. 3c . As final step, a control experiment wasperformed by using deionized water with a volume of 20 μL.

Incubation with the FGF-2 molecules in a volume of 10 μL changes theeffective permittivity of the biosensor (1). The change corresponding tothis situation is a 3.5% decrease in resonant frequency. Adding heparin(H) molecules caused a further decrease in resonant frequency since theincrease in permittivity due to the heparin (H) molecules binding theFGF-2 molecules. Resonant frequency change measured upon adding heparinmolecules in concentration of 10 μg/ml was as 10%. The decrease inresonant frequency is proportional with the increase in the molecularconcentration of heparin (H). A control experiment with deionized waterbrought the resonant frequency to the value incubated with the FGF-2molecules. From these results, it is evident that the effect ofmolecular interaction on biosensor (1) response was measured.

The change in resonant frequency relative to molecular concentration isgiven in FIG. 4. According to this graph, there is a linear dependencywithin measurement limits, and the sensitivity was measured as 3.7kHz/(ng/ml). It is possible to measure interaction between moleculeswith sub ng/ml levels with a frequency resolution of 1 kHz at themeasurement frequency band.

Using the inventive biosensor (1), in a method enabling the measurementof the transmission (s21) and reflection (s11) characteristics ofsplit-ring resonator (4), and in order to determine the concentration ofa desired molecule in a liquid in the medium the following steps areperformed: first probe molecules (for example FGF-2) in a certainconcentration are incubated on the surface of split-ring resonator (4)coated with a dielectric layer. In order to coat the split-ringresonator (4) area subjected to incubation with the said probe molecules(for example FGF-2) uniformly, a droplet in a certain volume is placedon a certain location on the split-ring resonator (4) at roomtemperature and left for a predetermined period of time. Second, thesurface of the split-ring resonator (4) is dried, and a dropletcomprising a second molecule is placed (for example heparin (H)) in acertain volume and concentration. In order to measure the concentrationof molecule in the said droplet, first an electric signal is applied ontwo symmetrical antennas (5) which are coplanar with the split-ringresonator (4). The said electric signal is converted intoelectromagnetic wave by the antennas (5) and transmitted to thesplit-ring resonator (4), and the split-ring resonator (4) is excitedvia the said electromagnetic waves. Then, the transmission (s21) andreflection (s11) characteristics of split-ring resonator (4) aremeasured using a vector network analyzer connected to the antennas (5)through ports (6) of the biosensor (1).

In order to determine the concentration of a desired molecule in aliquid in the medium, transmission (s21) and reflection (s11)characteristics of split-ring resonator before the second molecule (forexample heparin (H)) is added to the medium are measured, and theobtained characteristics are compared. For this, first theabovementioned first step is performed. In first step, probe moleculesin a certain concentration (for example FGF-2) are incubated on thesurface of split-ring resonator (4) coated with a dielectric layer. Inorder to coat the split-ring resonator (4) is subjected to incubationwith the said probe molecules (for example FGF-2) uniformly, a dropletin a certain volume is placed on a certain location on the split-ringresonator (4) at room temperature and left for a predetermined period oftime. An electric signal is applied on two symmetrical antennas (5)which are coplanar with the split-ring resonator (4). The said electricsignal is converted into electromagnetic wave by the antennas (5) andtransmitted to the split-ring resonator (4), and the split-ringresonator (4) is excited via the said electromagnetic waves. Then, thetransmission (s21) and reflection (s11) characteristics of split-ringresonator (4) are measured with a vector network analyzer. The measuredcharacteristic is considered as a reference.

These reference characteristic values which are obtained are comparedwith the transmission (s21) and reflection (s11) characteristics of thesplit-ring resonator (4) after the second molecule is added to themedium. By referencing the shift in resonant frequency due to the secondmolecule added to the medium (which are towards lower frequencies), theconcentration of the second molecule in the medium (for example heparin(H)) is determined easily. This process is determined considering thecharacteristic values, which are recorded before in one embodiment ofthe invention. In another embodiment of the invention, the concentrationvalue of the second molecule in the medium is determined by calculatingthe shift in resonant frequency with respect to a control unit andcomparing with pre-recorded data.

We claim:
 1. A biosensor for measuring the concentration of a desired molecule inside a liquid medium, comprising: at least one metallic plate functioning as a ground plate; at least one dielectric substrate located on top of the at least one metallic plate; and at least one split-ring resonator realized on top of the at least one dielectric substrate, wherein the at least one split-ring resonator is a single split ring resonator; wherein, at least two symmetrical antennas are realized on a same plane with the at least one split-ring resonator on top of the at least one dielectric substrate and the at least two symmetrical antennas excite the at least one split-ring resonator by emitting electromagnetic waves, the metallic plate enables the electromagnetic waves emitted from the at least two symmetrical antennas to be transmitted to the at least one split-ring resonator by reflecting the electromagnetic waves, and at least two ports where a network analyzer is connected to the at least two symmetrical antennas.
 2. The biosensor according to claim 1, wherein the at least two symmetrical antennas are monopole patch antennas.
 3. The biosensor according to claim 1, wherein the at least two ports which enable the network analyzer connecting with the at least two symmetrical antennas via SMA connectors.
 4. The biosensor according to claim 1, wherein the at least one split-ring resonator and the at least two symmetrical antennas are metallic structures which are formed in order to be excited with a magnetic field perpendicular to its own plane at a resonant frequency known as magnetic resonance (f_(m)) and behaves as a LC resonator.
 5. The biosensor according to claim 1, wherein the at least one split-ring resonator is coated with a dielectric layer, the dielectric layer is a parylene layer, wherein the parylene layer is treated with oxygen plasma.
 6. The biosensor according to claim 1, wherein the at least one dielectric substrate is manufactured from FR4 material.
 7. The biosensor according to claim 1, wherein the at least one dielectric substrate is manufactured from alumina material.
 8. The biosensor according to claim 1, wherein the at least one dielectric substrate is manufactured from mica material.
 9. The biosensor according to claim 1, wherein the at least one metallic plate is manufactured from aluminum.
 10. The biosensor according to claim 1, wherein excitation by the at least two symmetrical antennas induce a current circulating around the at least one split-ring; wherein a resonant frequency fm is given by the following equation: ${f_{m} = \frac{1}{2\pi\sqrt{C_{eff}L_{eff}}}},{C_{eff} = {C_{g} + C_{s}}},$ where C_(eff) is an effective capacitance, and L_(eff) is an effective inductance; where ${C_{g} = {{ɛ_{eff}\frac{h\;\omega}{g}} + {ɛ_{eff}\left( {h + g + w} \right)}}},$ h and w are respectively the thickness and width of the metallic structure, and g is the slit gap; where ${C_{s} = {2ɛ_{eff}\frac{\left( {h + \omega} \right)}{\pi}{\ln\left( \frac{4r}{g} \right)}}},$ ε_(eff) is an effective permittivity of media surrounding the split-ring resonator, r is radius of the ring of the split-ring resonator.
 11. The biosensor according to claim 1, wherein the split-ring resonator is formed of a split metallic ring realized on top of the dielectric substrate. 